Answer:
$77, 456
Step-by-step explanation:
Let P(x) = profit
P(x) = revenue - cost
⇒ P(x) = (952x - 0.68x²) - (-153x + 371450)
⇒ P(x) = -0.68x² + 1105x - 371450
Differentiate P(x)
⇒ P'(x) = -1.36x + 1105
Set P'(x) = 0 and solve for x:
⇒ -1.36x + 1105 = 0
⇒ 1.36x = 1105
⇒ x = 812.5
Therefore, maximum profit when x = 812.5
Substitute x = 812.5 into P(x):
P(812.5) = -0.68(812.5)²+ 1105(812.5) - 371450 = 77456.25
